Preheat Oven. Preheat your oven to 350°F (175°C).
Prep Apples. Peel, core, and slice the apples into thin wedges. A few peels here and there is fine.
Make filling. In a large bowl, combine the apples, granulated sugar, brown sugar, cinnamon, nutmeg, lemon juice, flour, and salt. Toss until the apples are evenly coated.
Prebake filling. Pour the apple mixture into a 8 or 9 inch square or round baking dish, spreading it out evenly. Cover with foil (yes, just the filling!) and bake for 20 minutes.
Make the topping. In a medium mixing bowl, cream together the softened butter and granulated sugar until light and fluffy. Beat in the vanilla extract and the egg until well incorporated. Add the flour, baking powder, and salt. Gradually add the dry mixture to the butter mixture, mixing until just combined.
Spread Topping. Spoon the topping over the apples, spreading it gently with the back of a spoon or a spatula. It’s okay if the topping doesn't cover all the apples completely. Sprinkle coarse sugar over the topping for a crunchy finish.
Bake. Bake in the preheated oven for 30-35 minutes, or until the topping is golden brown and the apples are tender.
Serve. Let the cobbler cool for a few minutes before serving. Enjoy it warm, optionally with a scoop of vanilla ice cream or a dollop of whipped cream!